Prediction of the Direction of XFEM Crack Based on Von Mises Around the Crack-tip under Mode-I

The extended finite element method (XFEM) is now widely used in crack simulations and the direction of propagation of the XFEM crack in SS-304 has been quite interesting. This paper discusses the direction,θ(+ve in anti-clockwise direction), of the XFEM crack (under mode-I) propagation based on the von Mises stress-field around the crack-tip for static loading under the light water reactors (LWRs) conditions. The Mises core region from the crack-tip is chosen for β=〖90〗^o, the angle between the load and the initial crack. Experimental data for LWRs’environment is obtained and the simulations have been carried out applying three different static loads and results for the direction of the crack are calculated by measuring the stress-field around the crack-tip. It has been found that the direction of the XFEM varies inversely as the stress-field around the crack tip is increased. The computational results have been compared with the numerical results based on the minimum strain energy density criterion[S-criterion].

Modeling of Looping Behavior in a Flexible Instrument Using a Bélzier Curve

Flexible medical instruments undergo looping during insertion and navigation inside the human body. It makes the control of the distal end difficult and raises safety concerns. This paper proposes the minimum strain energy concept to get the deformed shape of a flexible instrument in three-dimensional space. A B\'{e}zier curve is used to define the trajectory of the deformed shape under different loading conditions and constraints. Looping behavior is studied for different end shortening conditions. The effect of end twist on looping behavior is studied. It is observed that end twist leads to early onset of out of plane deformation leading to looping. The strain energy plot gives an insight into the behavior of these instruments with respect to end shortening and twist. The strain energy plot shows the minimum value for $2\pi$ end twist. Therefore, the instrument tends to go for looping if the end twist is present. Force and torque characteristics are obtained which will lead to the design and control of these instruments. Force and torque plots show negative stiffness when the instrument is going for looping. The un-looping phenomenon is also discussed and a strategy is proposed to mitigate looping. The proposed modeling approach can be utilized to address the complex behavior of a flexible instrument in medical as well as in other industrial applications. The insight developed will help in designing and developing control for safe and reliable usage of flexible instruments in various domains.

Proposition and analysis of strut and tie models for short corbels from techniques of topology optimization

Reinforced concrete short corbels are components characterized to represent typical conditions of geometrical and static discontinuity. In general, the classical bending theory is not valid for their design. With the strut and tie method, a model of a self-balanced truss, a strategy of representation of the principal stress flow appears as a representation of the trajectories of the main stresses in these components. Within the context of obtaining the strut and tie models, topology optimization is an indicated technique for an automated process. Combined with a numerical analysis based on finite elements, the SIMP (Solid Isotropic Material with Penalization) method formulation, which is defined with the criterion of minimum strain energy restricted by the volumetric fraction, is used for the development of the models with the ABAQUS® v. 6.14.1 software. Therefore, with the material distribution posterior to the optimization and the validation based on normative codes, it is demonstrated that the tool is effective in the development of strut and tie models.

ON THE OPTIMAL STRUT-AND-TIE MODELS AND DESIGN APPROACH FOR THE CABLE-PYLON ANCHORAGE ZONE

The cable-pylon anchorage zone is a typical D-region in a cable-stayed bridge, for which there has been no uniform simplified design method until now. In this paper, based on the extensive statistics of actual projects, topology optimization techniques and principle of minimum strain energy, two precise strut-and-tie models for the cable-pylon anchorage zone are proposed, which can clearly reveal the load-transmitting mechanism of the anchorage zone. Th e explicit geometric parameters of the strut-and-tie models are derived; thus, the designers can directly use these models. A simple design procedure to deploy prestressing tendons in the anchorage zone is also introduced, whose effectiveness and convenience are demonstrated by two design examples. A new design named the “one-way prestressing tendons PC cable-pylon” is also discussed regarding its application scope.

A Framework for Energy-Based Kinetostatic Modeling of Compliant Mechanisms

Although energy-based methods have advantages over the Newtonian methods for kinetostatic modeling, the geometric nonlinearities inherent in deflections of compliant mechanisms preclude most of the energy-based theorems. Castigliano’s first theorem and the Crotti-Engesser theorem, which don’t require the problem being solved to be linear, are selected to construct the energy-based kinetostatic modeling framework for compliant mechanisms in this work. Utilization of these two theorems requires explicitly formulating the strain energy in terms of deflections and the complementary strain energy in terms of loads, which are derived based on the beam constraint model. The kinetostatic modeling of two compliant mechanisms are provided to demonstrate the effectiveness of using Castigliano’s first theorem and the Crotti-Engesser theorem with the explicit formulations in this framework. Future work will be focused on incorporating use of the principle of minimum strain energy and the principle of minimum complementary strain energy.

Multi-Functional Topology Optimization of Piezoresistive Nanocomposite Beams

This paper presents an analysis of optimization for multifunctional nanocomposites. A carbon nanotubeepoxy composite is optimized for maximum resistance change and minimum strain energy. Analysis uses a finite element method and includes the coupled physics of mechanics, electrostatics, and piezoresistivity. The problem is solved first for minimum strain energy, then two resistance maximization problems are solved. For all optimization, sensitivities are obtained analytically. After solving the individual problems a weighted sum approach is used in the multi-objective optimization of both minimizing the strain energy and maximizing the resistance change. Comments are made as to the effect of the topology optimization method as a design tool, on the shape of the optimized cross sections, and on the possible extensions on using the coupled physics topology optimization algorithm.

Optimization Research on Geometric Parameters of Scallop-Shaped Lattice Shells

<p>Free-form and bionic spatial shells are popular in the area of spatial structures. Scallop-shaped surface is the product of evolution and a kind of spatial shells that can satisfy the mechanical requirements. Based on the scallop-shaped lattice shells, this paper focused on the optimization of geometric parameters. The principle of minimum strain energy was applied to conclude the influence law of the geometric parameters on mechanical properties. Finally the optimal values of geometric parameters were obtained. The results show that the optimization of geometric parameters presents the integrated significance to improve scallop-shaped lattice shells.</p>

Analytical Calculation Method for the Preliminary Analysis of Self-Anchored Suspension Bridges

The stiffening girder of self-anchored suspension bridge (SSB) is subjected to huge axial force because the main cable is directly anchored on the end of the stiffening girder. To obtain a simple model and accurately understand the mechanical behavior of the whole structure in preliminary design, this paper proposed an analytical calculation method considering the combined effects of the main cable-suspender-stiffening girder. On the basis of the deflection theory of the stiffening girder, the relation between the girder shape and the suspender force was explored. The relation between the main cable end force (MCEF) and the suspender force was derived through segmental catenary theory, and iteration method was further improved to avoid the divergence condition. Finally the solution was obtained through satisfying the compatibility condition. The proposed method does not need to iterate manually and can save calculation time. Examples are introduced to verify the applicability of this method, with the result that this method considers the combined effects of the main cable-suspender-stiffening girder, and the finished bridge state satisfies the minimum strain energy of the stiffening girder. Results also indicate that this method has fast convergence speed and high precision.